Both the prepositions عِنْدَ and مَعَ mean with but there is a difference between their use.

• When we say الْطَالِبُ عِنْدَ الْمُدِيْرِ "The student is with the headmaster" it means 'the student has gone to the headmaster's office and he is with him there, but

• When we say  الْطَالِبُ مَعَ الْمُدَرِّسِ "The student is with the teacher" it means there is no such restriction of being into the teacher's office i.e., the student can be with the teacher anywhere.

• The word عِنْدَ when used for a living thing it means with but when used for a non living thing it means near e.g., if we say بِيْتِيِ عِنْدَ مَسْجِدٍ it means my house is near a mosque.

• The word عِنْدَ is also used to convey the idea of 'to have' e.g., أَعِنْدَكَ كُرْسِيٌّ؟ 'Do you have a chair?' (literally, 'Is there a chair with you?')

The letter "بـِ" means at or in e.g., if we say 'هُوَ بِالْجَامِعَةِ' it means "He is at the university" or 'هِيَ بِالْمَطْبَخِ' it means she is in the kitchen.

It however must be remembered that "عِنْدَ" meaning 'to have'  should only be used with the things which are separable. It should not be used with relations and parts of the body. So if we want to say 'He has a nose' it should be said "لَهُ أَنْفٌ" instead of "عِنْدهُ أَنْفٌ"  or "لَهَا أُخْتٌ" meaning she has a sister. The preposition "لـَ" takes accusative case i.e., a fatha on it when used with all the pronouns except "يِ" meaning "mine". When used with 'يِ' it takes genitive case instead of the accusative case so it will become "لِيْ" so it will be said "لِيْ أَخٌ" and not "لَيْ أَخٌ"